Problem: If $f(x) = 3-\!\sqrt{x}$ and $g(x) = 5x +2x^2$, what is $f(g(-5))$?
Solution: We have $g(-5) = 5(-5) + 2(-5)^2 = -25 + 50 = 25$, so $f(g(-5)) = f(25) = 3 - \!\sqrt{25} = 3-5=\boxed{-2}$.